There is growing evidence for the effectiveness of choice architecture or ‘nudge’ interventions to change a range of behaviours including the consumption of alcohol, tobacco and food. Public acceptability is key to implementing these and other interventions. However, few studies have assessed public acceptability of these interventions, including the extent to which acceptability varies with the type of intervention, the target behaviour and with evidence of intervention effectiveness. These were assessed in an online study using a between-participants full factorial design with three factors: Policy (availability vs size vs labelling vs tax) x Behaviour (alcohol consumption vs tobacco use vs high-calorie snack food consumption) x Evidence communication (no message vs assertion of policy effectiveness vs assertion and quantification of policy effectiveness [e.g., a 10% change in behaviour]). Participants (N = 7058) were randomly allocated to one of the 36 groups. The primary outcome was acceptability of the policy. Acceptability differed across policy, behaviour and evidence communication (all ps < .001). Labelling was the most acceptable policy (supported by 78%) and Availability the least (47%). Tobacco use was the most acceptable behaviour to be targeted by policies (73%) compared with policies targeting Alcohol (55%) and Food (54%). Relative to the control group (60%), asserting evidence of effectiveness increased acceptability (63%); adding a quantification to this assertion did not significantly increase this further (65%). Public acceptability for nudges and taxes to improve population health varies with the behaviour targeted and the type of intervention but is generally favourable. Communicating that these policies are effective can increase support by a small but significant amount, suggesting that highlighting effectiveness could contribute to mobilising public demand for policies. While uncertainty remains about the strength of public support needed, this may help overcome political inertia and enable action on behaviours that damage population and planetary health.